A Theoretical Analysis of One-Dimensional Nonsteady Muscular Contraction

Most of the existing theories of muscle contraction rely primarily on specific information of the internal function of the system. These theories are generally based on mechanics or chemical kinetics models. We have previously proposed a general theory based on the laws of irreversible thermodynamics that requires only a general knowledge of the physical system. The theory has been derived in a form that is applicable to the three-dimensional, nonuniform, unsteady contraction of muscle. With a knowledge of the general physical parameters of the system, the solution of the equations would specify the force and shortening at each point in the muscle as a function of space and time. So far, we have solved the specific problem of the overall contraction of a uniform element of contractile material constrained to contract isometrically [1]. Presented herein is the response within a one-dimensional element of muscle rigidly attached at one end and acted upon by a sinusoidal force at the other end. The solution indicates that force and shortening within the muscle are composed mathematically of two sinusoidal waves moving in opposite directions. It is also seen that the maximum absolute value of the transfer function (from force to shortening) corresponds to an optimum physiological condition, where the passive elastic and active contractile responses combine to produce maximum work output. This suggests that a muscle at its optimum contractile state will shorten, against the same external force, a greater amount than when it was at a different contractile state. Application of the scheme of analysis to general nonsteady contractions of muscle, including the myocardium, is also indicated.